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Sylvain Capponi

Publications and source records attributed to Sylvain Capponi.

69 records · Page 4Linked to original sources
arXiv2006

Parity law of the singlet-triplet gap in graphitic ribbons

This work explores the possibility to transfer the parity law of the singlet-triplet gap established for square ladders (gapped for even number of legs, gapless for odd number of legs) to fused polyacenic 1-D systems, i.e., graphite ribbons. Qualitative arguments are presented in favor of a gapped character when the number $n\_ω$ of benzene rings along the ribbon width is odd. A series of numerical calculations (quantitative mapping on spin 1/2 chains, renormalized excitonic treatments and Quantum Monte Carlo) confirm the parity law and the gapless character of the ribbon for even $n\_ω$.

cond-mat.str-el↗
arXiv2006

Bond order wave instabilities in doped frustrated antiferromagnets: "Valence bond solids" at fractional filling

We explore both analytically and numerically the properties of doped t-J models on a class of highly frustrated lattices, such as the kagome and the pyrochlore lattice. Focussing on a particular sign of the hopping integral and antiferromagnetic exchange, we find a generic symmetry breaking instability towards a twofold degenerate ground state at a fractional filling below half filling. These states show modulated bond strengths and only break lattice symmetries. They can be seen as a generalization of the well-known valence bond solid states to fractional filling.

cond-mat.str-el↗
arXiv2006

Bond-order modulated staggered flux phase for the $t{-}J$ model on the square lattice

Motivated by the observation of inhomogeneous patterns in some high-T$_c$ cuprate compounds, several variational Gutzwiller-projected wave-functions with built-in charge and bond order parameters are proposed for the extended $t-J-V$ model on the square lattice at low doping. First, following a recent Gutzwiller-projected mean-field approach by one of us (Phys. Rev. B. {\bf 72}, 060508(R) (2005)), we investigate, as a function of doping and Coulomb repulsion, the stability of the staggered flux phase with respect to small spontaneous modulations of squared unit cells ranging from $2\times 2$ to $\sqrt{32}\times\sqrt{32}$. It is found that a $4\times 4$ bond-order (BO) modulation appears spontaneously on top of the staggered flux pattern for hole doping around 1/8. A related wave-function is then constructed and optimized accurately and its properties studied extensively using an approximation-free variational Monte Carlo scheme. Finally, the competition of the BO-modulated staggered flux wave-function w.r.t. the d-wave RVB wave-function or the commensurate flux state is investigated. It is found that a short range Coulomb repulsion penalizes the d-wave superconductor and that a moderate Coulomb repulsion brings them very close in energy. Our results are discussed in connection to the STM observations in the under-doped regime of some cuprates.

cond-mat.str-el↗
arXiv2005

Numerical Contractor Renormalization applied to strongly correlated systems

We demonstrate the utility of effective Hamilonians for studying strongly correlated systems, such as quantum spin systems. After defining local relevant degrees of freedom, the numerical Contractor Renormalization (CORE) method is applied in two steps: (i) building an effective Hamiltonian with longer ranged interactions up to a certain cut-off using the CORE algorithm and (ii) solving this new model numerically on finite clusters by exact diagonalization and performing finite-size extrapolations to obtain results in the thermodynamic limit. This approach, giving complementary information to analytical treatments of the CORE Hamiltonian, can be used as a semi-quantitative numerical method to study frustrated magnets (as the S=1/2 kagome lattice) or doped systems.

cond-mat.str-el↗
arXiv2004

Global Phase Diagram of the High Tc Cuprates

The high Tc cuprates have a complex phase diagram with many competing phases. We propose a bosonic effective quantum Hamiltonian based on the projected SO(5) model with extended interactions, which can be derived from the microscopic models of the cuprates. The global phase diagram of this model is obtained using mean-field theory and the Quantum Monte Carlo simulation, which is possible because of the absence of the minus sign problem. We show that this single quantum model can account for most salient features observed in the high Tc cuprates, with different families of the cuprates attributed to different traces in the global phase diagram. Experimental consequences are discussed and new theoretical predictions are presented.

cond-mat.supr-con↗
arXiv2004

Numerical Contractor Renormalization Method for Quantum Spin Models

We demonstrate the utility of the numerical Contractor Renormalization (CORE) method for quantum spin systems by studying one and two dimensional model cases. Our approach consists of two steps: (i) building an effective Hamiltonian with longer ranged interactions using the CORE algorithm and (ii) solving this new model numerically on finite clusters by exact diagonalization. This approach, giving complementary information to analytical treatments of the CORE Hamiltonian, can be used as a semi-quantitative numerical method. For ladder type geometries, we explicitely check the accuracy of the effective models by increasing the range of the effective interactions. In two dimensions we consider the plaquette lattice and the kagome lattice as non-trivial test cases for the numerical CORE method. On the plaquette lattice we have an excellent description of the system in both the disordered and the ordered phases, thereby showing that the CORE method is able to resolve quantum phase transitions. On the kagome lattice we find that the previously proposed twofold degenerate S=1/2 basis can account for a large number of phenomena of the spin 1/2 kagome system. For spin 3/2 however this basis does not seem to be sufficient anymore. In general we are able to simulate system sizes which correspond to an 8x8 lattice for the plaquette lattice or a 48-site kagome lattice, which are beyond the possibilities of a standard exact diagonalization approach.

cond-mat.str-el↗
arXiv2004

Current Carrying Ground State in a Bi-layer Model

Strongly interacting systems have been conjectured to spontaneously develop current carrying ground states under certain conditions. We conclusively demonstrate the existence of a commensurate staggered interlayer current phase in a bi-layer model by using the recently discovered quantum Monte-Carlo algorithm without the sign problem. A pseudospin SU(2) algebra and the corresponding anisotropic spin-1 Heisenberg model are constructed to show the competition among the staggered interlayer current, rung singlet and charge density wave phases.

cond-mat.str-el↗
arXiv2003

Superconducting gap for a 2-leg t-J ladder

Single-particle diagonal and off-diagonal Green's functions of a 2-leg t-J ladder at 1/8-doping are investigated by Exact Diagonalisations techniques. A numerically tractable expression for the superconducting gap is proposed and the frequency dependence of the real and imaginary parts of the gap are determined. The role of the low-energy gapped spin modes whose energies are computed by a (one-step) Contractor Renormalization procedure are discussed.

cond-mat.str-el↗
arXiv2002

Charge density correlations in t-J ladders investigated by the CORE method

Using 4-site plaquette or rung basis decomposition, the CORE method is applied to 2-leg and 4-leg t-J ladders and cylinders. Resulting range-2 effective hamiltonians are studied numerically on periodic rings taking full advantage of the translation symmetry as well as the drastic reduction of the Hilbert space. We investigate the role of magnetic and fermionic degrees of freedom to obtain the most reliable representation of the underlying model. Spin gaps, pair binding energies and charge correlations are computed and compared to available ED and DMRG data for the full Hamiltonian. Strong evidences for short-range diagonal stripe correlations are found in periodic 4-leg t-J ladders.

cond-mat.str-el↗
arXiv2002

Finite Size Scaling of the Spin Stiffness of the Antiferromagnetic S=1/2 XXZ chain

We study the finite size scaling of the spin stiffness for the one-dimensional s=1/2 quantum antiferromagnet as a function of the anisotropy parameter Delta.Previous Bethe ansatz results allow a determination of the stiffness in the thermodynamic limit. The Bethe ansatz equations for finite systems are solvable even in the presence of twisted boundary conditions, a fact we exploit to determine the stiffness exactly for finite systems allowing for a complete determination of the finite size corrections. Relating the stiffness to thermodynamic quantities we calculate the temperature dependence of the susceptibility and its finite size corrections at T=0. A Luttinger liquid approach is used to study the finite size corrections using renormalization group techniques and the results are compared to the numerically exact results obtained using the Bethe ansatz equations. Both irrelevant and marginally irrelevant cases are considered.

cond-mat.str-el↗
arXiv2001

Low-frequency current fluctuations in doped ladders

Charge current static and dynamical correlations are computed by exact diagonalisation methods on a 2-leg t-t'-J ladder which exhibits a sharp transition between a Luther-Emery (LE) phase of hole pairs and a phase with deconfined holes. In the LE phase, we find short-range low-energy incommensurate current fluctuations which are intrinsically connected to the internal charge dynamics within one hole pair. On the contrary, when holes unbind, the maximum of the current susceptibility moves abruptly to the commensurate wavevector $π$ and strongly increases for decreasing doping suggesting an instability towards a staggered flux state at sufficiently small doping.

cond-mat.str-el↗
arXiv2001

Single hole dynamics in the t-J model on two- and three-leg ladders

The dynamics of a single hole in the t-J model on two- (2LL) and three- (3LL) leg ladders is studied using a recently developed quantum Monte Carlo algorithm. For the 2LL it is shown that in addition to the most pronounced features of the spectral function, well described by the limit of strong coupling along the rungs, a clear shadow band appears in the antibonding channel. Moreover, both the bonding band and its shadow have a finite quasiparticle (QP) weight in the thermodynamic limit. For strong coupling along the rungs of the 3LL, the low-energy spectrum in the antisymmetric channel is similar to a one-dimensional chain, whereas in the two symmetric channels it resembles the 2LL. The QP weight vanishes in the antisymmetric channel, but is finite in the symmetric one.

cond-mat.str-el↗
arXiv1999

Effects of Long Range Electronic Interactions on a One-dimensional Electron System

The effects of a long range electronic potential on a one dimensional chain of spinless fermions are investigated by numerical techniques (Exact Diagonalisation of rings with up to 30 sites complemented by finite size analysis) and analytic calculations. Due to a competition between the $2 k_F$ oscillations in the density and the (very slow) log divergence of the long wavelength part of the Coulomb potential, the metallic character of the system is enhanced at intermediate (and up to quite large) lengthscales. Despite some similarities, we found that this quasi-metallic regime is not of the Luttinger Liquid type, as evidenced by strong deviations from predictions of conformal field theory and in agreement with the picture of a (very weakly pinned) Wigner crystal. When the strength of the Coulomb interaction is substancially increased, we observe a smooth cross-over to a strongly localized charge density wave.

cond-mat.str-el↗
arXiv1997

Persistent currents in a Moebius ladder: A test of interchain coherence of interacting electrons

Persistent currents in a Moebius ladder are shown to be very sensitive to the effects of intrachain interactions on the hopping of electrons between chains. Their periodicity as a function of flux is doubled for strong enough repulsive interactions because electrons cannot hop coherently between the chains and have to travel along the full edge of the Moebius ladder, thus encircling the flux twice. Mesoscopic devices that should enable one to observe these effects are proposed.

cond-mat.str-el↗